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<h4 class="mume-header" id="%E4%BF%A1%E6%81%AF%E9%87%8F">&#x4FE1;&#x606F;&#x91CF;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">I</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">f</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">n</mi></mrow><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mi>log</mi><mo>&#x2061;</mo><mfrac><mn>1</mn><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mfrac><mo>=</mo><mo>&#x2212;</mo><mi>log</mi><mo>&#x2061;</mo><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathrm{Information}(x) = \log \dfrac{1}{p(x)} = -\log p(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">I</span><span class="mord mathrm">n</span><span class="mord mathrm" style="margin-right:0.07778em;">f</span><span class="mord mathrm">o</span><span class="mord mathrm">r</span><span class="mord mathrm">m</span><span class="mord mathrm">a</span><span class="mord mathrm">t</span><span class="mord mathrm">i</span><span class="mord mathrm">o</span><span class="mord mathrm">n</span></span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.25744em;vertical-align:-0.936em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">&#x2212;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span></span></p>
<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">p(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span>&#x8868;&#x793A;&#x67D0;&#x4E00;&#x4E8B;&#x4EF6;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span></span></span></span>&#x5176;&#x5B50;&#x60C5;&#x51B5;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">x</span></span></span></span>&#x53D1;&#x751F;&#x7684;&#x6982;&#x7387;&#x3002;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">p(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span>&#x8D8A;&#x5927;&#xFF0C;&#x4FE1;&#x606F;&#x91CF;&#x8D8A;&#x5C0F;&#x3002;</p>
<h4 class="mume-header" id="%E4%BF%A1%E6%81%AF%E7%86%B5">&#x4FE1;&#x606F;&#x71B5;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mi>X</mi><mo stretchy="false">)</mo><mo>=</mo><mo>&#x2212;</mo><munder><mo>&#x2211;</mo><mrow><mi>x</mi><mo>&#x2208;</mo><mi>X</mi></mrow></munder><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>&#x22C5;</mo><mi>log</mi><mo>&#x2061;</mo><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathrm{Entropy}(X) = -\sum_{x&#x2208;X} p(x) &#x22C5; \log p(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.3717110000000003em;vertical-align:-1.321706em;"></span><span class="mord">&#x2212;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.8556639999999998em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="mrel mtight">&#x2208;</span><span class="mord mathdefault mtight" style="margin-right:0.07847em;">X</span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.321706em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span></span></p>
<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span></span></span></span>&#x6307;&#x67D0;&#x4E00;&#x4E8B;&#x4EF6;&#xFF0C;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">x</span></span></span></span>&#x904D;&#x5386;&#x4E86;&#x5176;&#x6240;&#x6709;&#x5B50;&#x60C5;&#x51B5;&#xFF0C;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">p(x)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span>&#x6307;&#x67D0;&#x4E00;&#x5B50;&#x60C5;&#x51B5;&#x53D1;&#x751F;&#x7684;&#x6982;&#x7387;&#x3002;&#x8BE5;&#x503C;&#x8868;&#x8FBE;&#x4E86;&#x4E8B;&#x4EF6;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span></span></span></span>&#x7684;&#x4E0D;&#x786E;&#x5B9A;&#x6027;&#xFF0C;<span class="highlight">&#x71B5;&#x8D8A;&#x5927;&#xFF0C;&#x4E0D;&#x786E;&#x5B9A;&#x6027;&#x8D8A;&#x5927;</span>&#x3002;</p>
<p><span class="highlight">&#x4FE1;&#x606F;&#x71B5;&#x4EA6;&#x662F;&#x5EA6;&#x91CF;&#x6837;&#x672C;&#x7EAF;&#x5EA6;&#x5730;&#x6307;&#x6807;&#xFF0C;&#x8BE5;&#x503C;&#x8D8A;&#x5C0F;&#xFF0C;&#x6837;&#x672C;&#x7EAF;&#x5EA6;&#x8D8A;&#x9AD8;&#xFF0C;&#x5373;&#x6837;&#x672C;&#x4E2D;&#x5C3D;&#x53EF;&#x80FD;&#x5C5E;&#x4E8E;&#x540C;&#x4E00;&#x7C7B;&#x522B;&#x3002;</span></p>
<div class="hint">
<p>&#x4EA4;&#x53C9;&#x71B5;&#xFF1A;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">C</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mi>p</mi><mo separator="true">,</mo><mi>q</mi><mo stretchy="false">)</mo><mo>=</mo><munder><mo>&#x2211;</mo><mi>x</mi></munder><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>&#x22C5;</mo><mi>log</mi><mo>&#x2061;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mrow><mi>q</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mfrac></mstyle></mrow><annotation encoding="application/x-tex">\mathrm{CrossEntropy}(p, q) = \sum\limits_{x} p(x) &#x22C5; \log \dfrac{1}{q(x)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">C</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">s</span><span class="mord mathrm">s</span><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord mathdefault">p</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">q</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1.70001em;vertical-align:-0.950005em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.750005em;"><span style="top:-2.149995em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.950005em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.25744em;vertical-align:-0.936em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">q</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>p</mi></mrow><annotation encoding="application/x-tex">p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">p</span></span></span></span>&#xFF1A;&#x771F;&#x5B9E;&#x5206;&#x5E03;</li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">q</span></span></span></span>&#xFF1A;&#x975E;&#x771F;&#x5B9E;&#x5206;</li>
</ul>
<p>&#x8BE5;&#x5F0F;&#x7528;&#x4E8E;&#x5EA6;&#x91CF;&#x4E24;&#x4E2A;&#x6982;&#x7387;&#x5206;&#x5E03;&#x95F4;&#x7684;&#x5DEE;&#x5F02;&#x6027;&#x4FE1;&#x606F;&#x3002;</p>
</div>
<h4 class="mume-header" id="%E6%9D%A1%E4%BB%B6%E7%86%B5">&#x6761;&#x4EF6;&#x71B5;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mi>Y</mi><mo>&#x21D0;</mo><mi>X</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mi>Y</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>X</mi><mo stretchy="false">)</mo><mtable rowspacing="0.15999999999999992em" columnalign="left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><munder><mo>&#x2211;</mo><mrow><mi>x</mi><mo>&#x2208;</mo><mi>X</mi></mrow></munder><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>&#x22C5;</mo><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mi>Y</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>X</mi><mo>=</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mo>&#x2212;</mo><munder><mo>&#x2211;</mo><mrow><mi>x</mi><mo>&#x2208;</mo><mi>X</mi></mrow></munder><mi>p</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><munder><mo>&#x2211;</mo><mrow><mi>y</mi><mo>&#x2208;</mo><mi>Y</mi></mrow></munder><mi>p</mi><mo stretchy="false">(</mo><mi>y</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>x</mi><mo stretchy="false">)</mo><mo>&#x22C5;</mo><mi>log</mi><mo>&#x2061;</mo><mi>p</mi><mo stretchy="false">(</mo><mi>y</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>x</mi><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\mathrm{Entropy}(Y &#x21D0; X) = 
    \mathrm{Entropy}(Y {\ \bold\vert\ } X)
    \begin{array}{l}
    \\
    \\  = \sum\limits_{x&#x2208;X} p(x) &#x22C5; \mathrm{Entropy}(Y {\ \bold\vert\ } X=x) 
    \\  = -\sum\limits_{x&#x2208;X} p(x) \sum\limits_{y&#x2208;Y}
                p(y {\ \bold\vert\ } x)
                &#x22C5; 
                \log p(y {\ \bold\vert\ } x)
    \end{array}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x21D0;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:6.232150000000001em;vertical-align:-2.8660750000000004em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.366075em;"><span style="top:-5.526075em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-4.3260749999999994em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-3.1260749999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.750005em;"><span style="top:-2.105664em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="mrel mtight">&#x2208;</span><span class="mord mathdefault mtight" style="margin-right:0.07847em;">X</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.021706em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span><span style="top:-1.2643689999999996em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">&#x2212;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.750005em;"><span style="top:-2.105664em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">x</span><span class="mrel mtight">&#x2208;</span><span class="mord mathdefault mtight" style="margin-right:0.07847em;">X</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.021706em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.7500050000000001em;"><span style="top:-2.105664em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">y</span><span class="mrel mtight">&#x2208;</span><span class="mord mathdefault mtight" style="margin-right:0.22222em;">Y</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.130444em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x22C5;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">p</span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">x</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:2.8660750000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span></span></span></span></span></p>
<p>&#x5DF2;&#x77E5;&#x4E8B;&#x4EF6;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">X</span></span></span></span>&#x7684;&#x60C5;&#x51B5;&#x4E0B;&#x6C42;&#x4E8B;&#x4EF6;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.22222em;">Y</span></span></span></span>&#x7684;&#x4E0D;&#x786E;&#x5B9A;&#x6027;&#x3002;</p>
<h3 class="mume-header" id="%E4%BF%A1%E6%81%AF%E5%A2%9E%E7%9B%8A">&#x4FE1;&#x606F;&#x589E;&#x76CA;</h3>

<h4 class="mume-header" id="%E5%A2%9E%E7%9B%8A%E5%80%BC">&#x589E;&#x76CA;&#x503C;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mo separator="true">,</mo><mi>a</mi><mo stretchy="false">)</mo><mtable rowspacing="0.15999999999999992em" columnalign="left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mo stretchy="false">)</mo><mo>&#x2212;</mo><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mrow><mtext>&#xA0;</mtext><mi mathvariant="bold">&#x2223;</mi><mtext>&#xA0;</mtext></mrow><mi>a</mi><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mo stretchy="false">)</mo><mo>&#x2212;</mo><msubsup><mo>&#x2211;</mo><mrow><mi>v</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>a</mi><mi mathvariant="normal">.</mi><mi>V</mi></mrow></msubsup><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi mathvariant="normal">&#x2223;</mi><msup><mi>D</mi><mi>v</mi></msup><mi mathvariant="normal">&#x2223;</mi></mrow><mrow><mi mathvariant="normal">&#x2223;</mi><mi>D</mi><mi mathvariant="normal">&#x2223;</mi></mrow></mfrac></mstyle><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><msup><mi>D</mi><mi>v</mi></msup><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\mathrm{Gain}(D, a) 
\begin{array}{l}
\\
\\  = \mathrm{Entropy}(D) - \mathrm{Entropy}(D {\ \bold\vert\ } a)
\\  = \mathrm{Entropy}(D) - \sum\limits_{v=1}^{a.V} \dfrac{|D^v|}{|D|} \mathrm{Entropy}(D^v)
\end{array}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.095449000000001em;vertical-align:-2.7977245000000006em;"></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">a</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">a</span><span class="mclose">)</span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.2977245000000006em;"><span style="top:-5.986060500000002em;"><span class="pstrut" style="height:3.5283360000000004em;"></span><span class="mord"></span></span><span style="top:-4.7860605000000005em;"><span class="pstrut" style="height:3.5283360000000004em;"></span><span class="mord"></span></span><span style="top:-3.5860605000000003em;"><span class="pstrut" style="height:3.5283360000000004em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord"><span class="mspace">&#xA0;</span><span class="mord mathbf">&#x2223;</span><span class="mspace">&#xA0;</span></span><span class="mord mathdefault">a</span><span class="mclose">)</span></span></span><span style="top:-1.6977244999999996em;"><span class="pstrut" style="height:3.5283360000000004em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5283360000000004em;"><span style="top:-2.132887em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span><span style="top:-3.950005em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">.</span><span class="mord mathdefault mtight" style="margin-right:0.22222em;">V</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.9671129999999999em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord">&#x2223;</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span></span></span></span></span></span></span></span><span class="mord">&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:2.7977245000000006em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span></span></span></span></span></p>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span></span>&#xFF1A;&#x6570;&#x636E;&#x96C6;</li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">a</span></span></span></span>&#xFF1A;&#x67D0;&#x4E00;&#x79BB;&#x6563;&#x5C5E;&#x6027;</li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi><mi mathvariant="normal">.</mi><mi>V</mi></mrow><annotation encoding="application/x-tex">a.V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault">a</span><span class="mord">.</span><span class="mord mathdefault" style="margin-right:0.22222em;">V</span></span></span></span>&#xFF1A;&#x5C5E;&#x6027;&#x53EF;&#x53D6;&#x7684;&#x503C;&#x6570;&#x91CF;</li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>D</mi><mi>v</mi></msup></mrow><annotation encoding="application/x-tex">D^v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span></span></span></span></span></span></span></span></span></span></span>&#x5305;&#x542B;&#x4E86;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span></span></span></span>&#x4E2D;&#x6240;&#x6709;&#x5C5E;&#x6027;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>a</mi></mrow><annotation encoding="application/x-tex">a</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">a</span></span></span></span>&#x4E0A;&#x53D6;&#x503C;&#x4E3A;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>a</mi><mi>v</mi></msup></mrow><annotation encoding="application/x-tex">a^v</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.664392em;vertical-align:0em;"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span></span></span></span></span></span></span></span></span></span></span>&#x7684;&#x6837;&#x672C;&#x3002;</li>
</ul>
<p><span class="highlight">&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x8D8A;&#x5927;&#xFF0C;&#x5373;&#x4F7F;&#x7528;&#x8BE5;&#x5C5E;&#x6027;&#x8FDB;&#x884C;&#x5212;&#x5206;&#x65F6;&#xFF0C;&#x5BF9;&#x7EAF;&#x5EA6;&#x7684;&#x63D0;&#x5347;&#x8D8A;&#x5927;&#x3002;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x51C6;&#x5219;&#x5BF9;&#x53EF;&#x53D6;&#x503C;&#x6570;&#x76EE;&#x8F83;&#x591A;&#x7684;&#x5C5E;&#x6027;&#x6709;&#x6240;&#x504F;&#x597D;&#x3002;</span></p>
<h4 class="mume-header" id="%E5%A2%9E%E7%9B%8A%E7%8E%87">&#x589E;&#x76CA;&#x7387;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">R</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">o</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mo separator="true">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mo separator="true">,</mo><mi>a</mi><mo stretchy="false">)</mo></mrow><mrow><mrow><mi mathvariant="normal">I</mi><mi mathvariant="normal">V</mi></mrow><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\mathrm{GainRatio}(D, a) = \dfrac{\mathrm{Gain}(D, a)}{\mathrm{IV}(a)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">a</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">R</span><span class="mord mathrm">a</span><span class="mord mathrm">t</span><span class="mord mathrm">i</span><span class="mord mathrm">o</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.363em;vertical-align:-0.936em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">I</span><span class="mord mathrm" style="margin-right:0.01389em;">V</span></span><span class="mopen">(</span><span class="mord mathdefault">a</span><span class="mclose">)</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">a</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">a</span><span class="mclose">)</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mi>V</mi></mrow><annotation encoding="application/x-tex">IV</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">I</span><span class="mord mathdefault" style="margin-right:0.22222em;">V</span></span></span></span>&#xFF1A;&#x5C5E;&#x6027;&#x7684;&#x56FA;&#x6709;&#x503C;&#xFF08;Intrinsic Value&#xFF09;</li>
</ul>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mi>V</mi><mo stretchy="false">(</mo><mi>a</mi><mo stretchy="false">)</mo><mo>=</mo><mo>&#x2212;</mo><munderover><mo>&#x2211;</mo><mrow><mi>v</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>a</mi><mi mathvariant="normal">.</mi><mi>V</mi></mrow></munderover><mfrac><mrow><mi mathvariant="normal">&#x2223;</mi><msup><mi>D</mi><mi>v</mi></msup><mi mathvariant="normal">&#x2223;</mi></mrow><mrow><mi mathvariant="normal">&#x2223;</mi><mi>D</mi><mi mathvariant="normal">&#x2223;</mi></mrow></mfrac><mi>log</mi><mo>&#x2061;</mo><mfrac><mrow><mi mathvariant="normal">&#x2223;</mi><msup><mi>D</mi><mi>v</mi></msup><mi mathvariant="normal">&#x2223;</mi></mrow><mrow><mi mathvariant="normal">&#x2223;</mi><mi>D</mi><mi mathvariant="normal">&#x2223;</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">IV(a) = 
        -\sum\limits_{v=1}^{a.V}
            \dfrac{|D^v|}{|D|}
            \log
            \dfrac{|D^v|}{|D|}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.07847em;">I</span><span class="mord mathdefault" style="margin-right:0.22222em;">V</span><span class="mopen">(</span><span class="mord mathdefault">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.0954490000000003em;vertical-align:-1.267113em;"></span><span class="mord">&#x2212;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x2211;</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">.</span><span class="mord mathdefault mtight" style="margin-right:0.22222em;">V</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord">&#x2223;</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span></span></span></span></span></span></span></span><span class="mord">&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord">&#x2223;</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span></span></span></span></span></span></span></span><span class="mord">&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p>
<p><span class="highlight">&#x589E;&#x76CA;&#x7387;&#x51C6;&#x5219;&#x5BF9;&#x53EF;&#x53D6;&#x503C;&#x6570;&#x76EE;&#x8F83;&#x5C11;&#x7684;&#x5C5E;&#x6027;&#x6709;&#x6240;&#x504F;&#x597D;&#x3002;</span></p>
<h4 class="mume-header" id="example">Example</h4>

<table>
<thead>
<tr>
<th>&#x7F16;&#x53F7;</th>
<th>&#x8272;&#x6CFD;</th>
<th>&#x6839;&#x8482;</th>
<th>&#x6572;&#x58F0;</th>
<th>&#x7EB9;&#x7406;</th>
<th>&#x8110;&#x90E8;</th>
<th>&#x89E6;&#x611F;</th>
<th>&#x597D;&#x74DC;</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>&#x9752;&#x7EFF;</td>
<td>&#x8737;&#x7F29;</td>
<td>&#x6D4A;&#x54CD;</td>
<td>&#x6E05;&#x6670;</td>
<td>&#x51F9;&#x9677;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x662F;</td>
</tr>
<tr>
<td>2</td>
<td>&#x4E4C;&#x9ED1;</td>
<td>&#x8737;&#x7F29;</td>
<td>&#x6C89;&#x95F7;</td>
<td>&#x6E05;&#x6670;</td>
<td>&#x51F9;&#x9677;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x662F;</td>
</tr>
<tr>
<td>3</td>
<td>&#x4E4C;&#x9ED1;</td>
<td>&#x8737;&#x7F29;</td>
<td>&#x6D4A;&#x54CD;</td>
<td>&#x6E05;&#x6670;</td>
<td>&#x51F9;&#x9677;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x662F;</td>
</tr>
<tr>
<td>4</td>
<td>&#x9752;&#x7EFF;</td>
<td>&#x8737;&#x7F29;</td>
<td>&#x6C89;&#x95F7;</td>
<td>&#x6E05;&#x6670;</td>
<td>&#x51F9;&#x9677;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x662F;</td>
</tr>
<tr>
<td>5</td>
<td>&#x6D45;&#x767D;</td>
<td>&#x8737;&#x7F29;</td>
<td>&#x6D4A;&#x54CD;</td>
<td>&#x6E05;&#x6670;</td>
<td>&#x51F9;&#x9677;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x662F;</td>
</tr>
<tr>
<td>6</td>
<td>&#x9752;&#x7EFF;</td>
<td>&#x7A0D;&#x8737;</td>
<td>&#x6D4A;&#x54CD;</td>
<td>&#x6E05;&#x6670;</td>
<td>&#x7A0D;&#x51F9;</td>
<td>&#x8F6F;&#x7C98;</td>
<td>&#x662F;</td>
</tr>
<tr>
<td>7</td>
<td>&#x4E4C;&#x9ED1;</td>
<td>&#x7A0D;&#x8737;</td>
<td>&#x6D4A;&#x54CD;</td>
<td>&#x7A0D;&#x7CCA;</td>
<td>&#x7A0D;&#x51F9;</td>
<td>&#x8F6F;&#x7C98;</td>
<td>&#x662F;</td>
</tr>
<tr>
<td>8</td>
<td>&#x4E4C;&#x9ED1;</td>
<td>&#x7A0D;&#x8737;</td>
<td>&#x6D4A;&#x54CD;</td>
<td>&#x6E05;&#x6670;</td>
<td>&#x7A0D;&#x51F9;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x662F;</td>
</tr>
<tr>
<td>9</td>
<td>&#x4E4C;&#x9ED1;</td>
<td>&#x7A0D;&#x8737;</td>
<td>&#x6C89;&#x95F7;</td>
<td>&#x7A0D;&#x7CCA;</td>
<td>&#x7A0D;&#x51F9;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x5426;</td>
</tr>
<tr>
<td>10</td>
<td>&#x9752;&#x7EFF;</td>
<td>&#x786C;&#x633A;</td>
<td>&#x6E05;&#x8106;</td>
<td>&#x6E05;&#x6670;</td>
<td>&#x5E73;&#x5766;</td>
<td>&#x8F6F;&#x7C98;</td>
<td>&#x5426;</td>
</tr>
<tr>
<td>11</td>
<td>&#x6D45;&#x767D;</td>
<td>&#x786C;&#x633A;</td>
<td>&#x6E05;&#x8106;</td>
<td>&#x6A21;&#x7CCA;</td>
<td>&#x5E73;&#x5766;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x5426;</td>
</tr>
<tr>
<td>12</td>
<td>&#x6D45;&#x767D;</td>
<td>&#x8737;&#x7F29;</td>
<td>&#x6D4A;&#x54CD;</td>
<td>&#x6A21;&#x7CCA;</td>
<td>&#x5E73;&#x5766;</td>
<td>&#x8F6F;&#x7C98;</td>
<td>&#x5426;</td>
</tr>
<tr>
<td>13</td>
<td>&#x9752;&#x7EFF;</td>
<td>&#x7A0D;&#x8737;</td>
<td>&#x6D4A;&#x54CD;</td>
<td>&#x7A0D;&#x7CCA;</td>
<td>&#x51F9;&#x9677;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x5426;</td>
</tr>
<tr>
<td>14</td>
<td>&#x6D45;&#x767D;</td>
<td>&#x7A0D;&#x8737;</td>
<td>&#x6C89;&#x95F7;</td>
<td>&#x7A0D;&#x7CCA;</td>
<td>&#x51F9;&#x9677;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x5426;</td>
</tr>
<tr>
<td>15</td>
<td>&#x4E4C;&#x9ED1;</td>
<td>&#x7A0D;&#x8737;</td>
<td>&#x6D4A;&#x54CD;</td>
<td>&#x6E05;&#x6670;</td>
<td>&#x7A0D;&#x51F9;</td>
<td>&#x8F6F;&#x7C98;</td>
<td>&#x5426;</td>
</tr>
<tr>
<td>16</td>
<td>&#x6D45;&#x767D;</td>
<td>&#x8737;&#x7F29;</td>
<td>&#x6D4A;&#x54CD;</td>
<td>&#x6A21;&#x7CCA;</td>
<td>&#x5E73;&#x5766;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x5426;</td>
</tr>
<tr>
<td>17</td>
<td>&#x9752;&#x7EFF;</td>
<td>&#x8737;&#x7F29;</td>
<td>&#x6C89;&#x95F7;</td>
<td>&#x7A0D;&#x7CCA;</td>
<td>&#x7A0D;&#x51F9;</td>
<td>&#x786C;&#x6ED1;</td>
<td>&#x5426;</td>
</tr>
</tbody>
</table>
<table>
<thead>
<tr>
<th>&#x597D;&#x74DC;</th>
<th>&#x574F;&#x74DC;</th>
</tr>
</thead>
<tbody>
<tr>
<td>8</td>
<td>9</td>
</tr>
</tbody>
</table>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mo stretchy="false">)</mo><mo>=</mo><mo>&#x2212;</mo><mrow><mo fence="true">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>8</mn><mn>17</mn></mfrac></mstyle><mi>log</mi><mo>&#x2061;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>8</mn><mn>17</mn></mfrac></mstyle><mo>+</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>9</mn><mn>17</mn></mfrac></mstyle><mi>log</mi><mo>&#x2061;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>9</mn><mn>17</mn></mfrac></mstyle><mo fence="true">)</mo></mrow><mo>=</mo><mn>0.998</mn></mrow><annotation encoding="application/x-tex">\mathrm{Entropy}(D) = -\left(
      \dfrac{8}{17}\log \dfrac{8}{17} + 
      \dfrac{9}{17}\log \dfrac{9}{17}
  \right) = 0.998</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="mord">&#x2212;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mord">7</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">8</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mord">7</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">8</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mord">7</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">9</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mord">7</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">9</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">9</span><span class="mord">9</span><span class="mord">8</span></span></span></span></li>
</ul>
<p><strong>&#x8BA1;&#x7B97;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mo separator="true">,</mo><mtext>&#x8272;&#x6CFD;</mtext><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathrm{Gain}(D, &#x8272;&#x6CFD;)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">a</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">&#x8272;</span><span class="mord cjk_fallback">&#x6CFD;</span><span class="mclose">)</span></span></span></span></strong></p>
<table>
<thead>
<tr>
<th>&#x8272;&#x6CFD;</th>
<th>&#x6570;&#x91CF;</th>
<th>&#x597D;&#x74DC;</th>
<th>&#x574F;&#x74DC;</th>
</tr>
</thead>
<tbody>
<tr>
<td>&#x9752;&#x7EFF;</td>
<td>6</td>
<td>3</td>
<td>3</td>
</tr>
<tr>
<td>&#x4E4C;&#x9ED1;</td>
<td>6</td>
<td>4</td>
<td>2</td>
</tr>
<tr>
<td>&#x6D45;&#x767D;</td>
<td>5</td>
<td>1</td>
<td>4</td>
</tr>
</tbody>
</table>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mtext>&#x8272;&#x6CFD;</mtext><mo>=</mo><mtext>&#x9752;&#x7EFF;</mtext><mo stretchy="false">)</mo><mo>=</mo><mo>&#x2212;</mo><mrow><mo fence="true">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>3</mn><mn>6</mn></mfrac></mstyle><mi>log</mi><mo>&#x2061;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>3</mn><mn>6</mn></mfrac></mstyle><mo>+</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>3</mn><mn>6</mn></mfrac></mstyle><mi>log</mi><mo>&#x2061;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>3</mn><mn>6</mn></mfrac></mstyle><mo fence="true">)</mo></mrow><mo>=</mo><mn>1</mn></mrow><annotation encoding="application/x-tex">\mathrm{Entropy}(&#x8272;&#x6CFD;=&#x9752;&#x7EFF;) = -\left(
      \dfrac{3}{6}\log \dfrac{3}{6} + 
      \dfrac{3}{6}\log \dfrac{3}{6}
  \right) = 1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord cjk_fallback">&#x8272;</span><span class="mord cjk_fallback">&#x6CFD;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord cjk_fallback">&#x9752;</span><span class="mord cjk_fallback">&#x7EFF;</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="mord">&#x2212;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">1</span></span></span></span></li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mtext>&#x8272;&#x6CFD;</mtext><mo>=</mo><mtext>&#x4E4C;&#x9ED1;</mtext><mo stretchy="false">)</mo><mo>=</mo><mo>&#x2212;</mo><mrow><mo fence="true">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>6</mn></mfrac></mstyle><mi>log</mi><mo>&#x2061;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>6</mn></mfrac></mstyle><mo>+</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>2</mn><mn>6</mn></mfrac></mstyle><mi>log</mi><mo>&#x2061;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>2</mn><mn>6</mn></mfrac></mstyle><mo fence="true">)</mo></mrow><mo>=</mo><mn>0.918</mn></mrow><annotation encoding="application/x-tex">\mathrm{Entropy}(&#x8272;&#x6CFD;=&#x4E4C;&#x9ED1;) = -\left(
      \dfrac{4}{6}\log \dfrac{4}{6} + 
      \dfrac{2}{6}\log \dfrac{2}{6}
  \right) = 0.918</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord cjk_fallback">&#x8272;</span><span class="mord cjk_fallback">&#x6CFD;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord cjk_fallback">&#x4E4C;</span><span class="mord cjk_fallback">&#x9ED1;</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="mord">&#x2212;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">9</span><span class="mord">1</span><span class="mord">8</span></span></span></span></li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mtext>&#x8272;&#x6CFD;</mtext><mo>=</mo><mtext>&#x6D45;&#x767D;</mtext><mo stretchy="false">)</mo><mo>=</mo><mo>&#x2212;</mo><mrow><mo fence="true">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>5</mn></mfrac></mstyle><mi>log</mi><mo>&#x2061;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>1</mn><mn>5</mn></mfrac></mstyle><mo>+</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>5</mn></mfrac></mstyle><mi>log</mi><mo>&#x2061;</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>5</mn></mfrac></mstyle><mo fence="true">)</mo></mrow><mo>=</mo><mn>0.722</mn></mrow><annotation encoding="application/x-tex">\mathrm{Entropy}(&#x8272;&#x6CFD;=&#x6D45;&#x767D;) = -\left(
      \dfrac{1}{5}\log \dfrac{1}{5} + 
      \dfrac{4}{5}\log \dfrac{4}{5}
  \right) = 0.722</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord cjk_fallback">&#x8272;</span><span class="mord cjk_fallback">&#x6CFD;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord cjk_fallback">&#x6D45;</span><span class="mord cjk_fallback">&#x767D;</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="mord">&#x2212;</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop">lo<span style="margin-right:0.01389em;">g</span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">7</span><span class="mord">2</span><span class="mord">2</span></span></span></span></li>
</ul>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtable rowspacing="0.15999999999999992em" columnalign="left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mo separator="true">,</mo><mtext>&#x8272;&#x6CFD;</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr></mtable><mtable rowspacing="0.15999999999999992em" columnalign="left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mo stretchy="false">)</mo><mo>&#x2212;</mo><msubsup><mo>&#x2211;</mo><mrow><mi>v</mi><mo>=</mo><mn>1</mn></mrow><mn>3</mn></msubsup><mstyle displaystyle="true" scriptlevel="0"><mfrac><mrow><mi mathvariant="normal">&#x2223;</mi><msup><mi>D</mi><mi>v</mi></msup><mi mathvariant="normal">&#x2223;</mi></mrow><mrow><mi mathvariant="normal">&#x2223;</mi><mi>D</mi><mi mathvariant="normal">&#x2223;</mi></mrow></mfrac></mstyle><mrow><mi mathvariant="normal">E</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">p</mi><mi mathvariant="normal">y</mi></mrow><mo stretchy="false">(</mo><msup><mi>D</mi><mi>v</mi></msup><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mn>0.998</mn><mo>&#x2212;</mo><mrow><mo fence="true">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>6</mn><mn>17</mn></mfrac></mstyle><mo>&#xD7;</mo><mn>1</mn><mo>+</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>6</mn><mn>17</mn></mfrac></mstyle><mo>&#xD7;</mo><mn>0.918</mn><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>5</mn><mn>17</mn></mfrac></mstyle><mo>&#xD7;</mo><mn>0.722</mn><mo fence="true">)</mo></mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mn>0.109</mn></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{array}{l}
    \mathrm{Gain}(D, &#x8272;&#x6CFD;) \\\\ \\\\ \\\\
\end{array}
\begin{array}{l}
        = \mathrm{Entropy}(D) - 
            \sum\limits_{v=1}^{3} \dfrac{|D^v|}{|D|} \mathrm{Entropy}(D^v)
\\\\    = 0.998 - \left(
            \dfrac{6}{17} &#xD7; 1 + 
            \dfrac{6}{17} &#xD7; 0.918
            \dfrac{5}{17} &#xD7; 0.722
        \right)
\\\\    = 0.109
\end{array}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:8.468256em;vertical-align:-3.984128000000001em;"></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.850000000000001em;"><span style="top:-6.010000000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">a</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord cjk_fallback">&#x8272;</span><span class="mord cjk_fallback">&#x6CFD;</span><span class="mclose">)</span></span></span><span style="top:-4.810000000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-3.6100000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-2.41em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.2100000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-0.009999999999999953em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:3.35em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:4.484128em;"><span style="top:-6.484128em;"><span class="pstrut" style="height:3.501113em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.5011130000000001em;"><span style="top:-2.132887em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">&#x2211;</span></span></span><span style="top:-3.950005em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">3</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.9671129999999999em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord">&#x2223;</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span></span></span></span></span></span></span></span><span class="mord">&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathrm">E</span><span class="mord mathrm">n</span><span class="mord mathrm">t</span><span class="mord mathrm">r</span><span class="mord mathrm">o</span><span class="mord mathrm">p</span><span class="mord mathrm" style="margin-right:0.01389em;">y</span></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-4.677015em;"><span class="pstrut" style="height:3.501113em;"></span><span class="mord"></span></span><span style="top:-2.867015em;"><span class="pstrut" style="height:3.501113em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">9</span><span class="mord">9</span><span class="mord">8</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mord">7</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mord">7</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">6</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">9</span><span class="mord">1</span><span class="mord">8</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mord">7</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#xD7;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">7</span><span class="mord">2</span><span class="mord">2</span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span></span></span><span style="top:-1.0769850000000003em;"><span class="pstrut" style="height:3.501113em;"></span><span class="mord"></span></span><span style="top:0.12301500000000082em;"><span class="pstrut" style="height:3.501113em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">1</span><span class="mord">0</span><span class="mord">9</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:3.984128000000001em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span></span></span></span></span></p>
<h3 class="mume-header" id="%E5%9F%BA%E5%B0%BC">&#x57FA;&#x5C3C;</h3>

<h4 class="mume-header" id="%E5%9F%BA%E5%B0%BC%E5%80%BC">&#x57FA;&#x5C3C;&#x503C;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mo stretchy="false">)</mo><mo>=</mo><munderover><mo>&#x2211;</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><munder><mo>&#x2211;</mo><mrow><msup><mi>k</mi><mo mathvariant="normal" lspace="0em" rspace="0em">&#x2032;</mo></msup><mo mathvariant="normal">&#x2260;</mo><mi>k</mi></mrow></munder><msub><mi>p</mi><mi>k</mi></msub><msub><mi>p</mi><msup><mi>k</mi><mo mathvariant="normal" lspace="0em" rspace="0em">&#x2032;</mo></msup></msub><mo>=</mo><mn>1</mn><mo>&#x2212;</mo><munderover><mo>&#x2211;</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msup><msub><mi>p</mi><mi>k</mi></msub><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\mathrm{Gini}(D) = \sum_{k=1}^{n} \sum_{k&apos;&#x2260;k} p_kp_{k&apos;} = 1 - \sum_{k=1}^{n} {p_k}^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">i</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.089618em;vertical-align:-1.438221em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6513970000000002em;"><span style="top:-1.8478869999999998em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x2211;</span></span></span><span style="top:-4.300005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.302113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.050005em;"><span style="top:-1.8478869999999998em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">&#x2032;</span></span></span></span></span></span></span></span></span><span class="mrel mtight"><span class="mrel mtight"><span class="mord mtight"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-2.7em;"><span class="pstrut" style="height:2.7em;"></span><span class="rlap mtight"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="inner"><span class="mrel mtight">&#xE020;</span></span><span class="fix"></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span><span class="mrel mtight">=</span></span><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x2211;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.438221em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathdefault">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6828285714285715em;"><span style="top:-2.786em;margin-right:0.07142857142857144em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">&#x2032;</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.9535100000000005em;vertical-align:-1.302113em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6513970000000002em;"><span style="top:-1.8478869999999998em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.0500049999999996em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x2211;</span></span></span><span style="top:-4.300005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.302113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord"><span class="mord"><span class="mord mathdefault">p</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.33610799999999996em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641079999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></p>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">n</span></span></span></span>&#xFF1A;&#x6837;&#x672C;&#x79CD;&#x7C7B;&#x6570;</li>
</ul>
<p><span class="highlight">&#x57FA;&#x5C3C;&#x503C;&#x53CD;&#x6620;&#x4E86;&#x4ECE;&#x6570;&#x636E;&#x96C6;&#x4E2D;&#x968F;&#x673A;&#x62BD;&#x53D6;&#x4E24;&#x4E2A;&#x6837;&#x672C;&#xFF0C;&#x5176;&#x7C7B;&#x522B;&#x6807;&#x8BB0;&#x4E0D;&#x4E00;&#x81F4;&#x7684;&#x6982;&#x7387;&#xFF08;&#x4E0D;&#x7EAF;&#x6027;&#x7684;&#x5EA6;&#x91CF;&#xFF09;&#x3002;&#x57FA;&#x5C3C;&#x503C;&#x8D8A;&#x5C0F;&#xFF0C;&#x6570;&#x636E;&#x96C6;&#x7EAF;&#x5EA6;&#x8D8A;&#x9AD8;&#x3002;</span></p>
<h4 class="mume-header" id="%E5%9F%BA%E5%B0%BC%E6%8C%87%E6%95%B0">&#x57FA;&#x5C3C;&#x6307;&#x6570;</h4>

<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">I</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi></mrow><mo stretchy="false">(</mo><mi>D</mi><mo separator="true">,</mo><mi>a</mi><mo stretchy="false">)</mo><mo>=</mo><munderover><mo>&#x2211;</mo><mrow><mi>v</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>a</mi><mi mathvariant="normal">.</mi><mi>V</mi></mrow></munderover><mfrac><mrow><mi mathvariant="normal">&#x2223;</mi><msup><mi>D</mi><mi>v</mi></msup><mi mathvariant="normal">&#x2223;</mi></mrow><mrow><mi mathvariant="normal">&#x2223;</mi><mi>D</mi><mi mathvariant="normal">&#x2223;</mi></mrow></mfrac><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi></mrow><mo stretchy="false">(</mo><msup><mi>D</mi><mi>v</mi></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathrm{GiniIndex}(D, a) = \sum_{v=1}^{a.V} \dfrac{|D^{v}|}{|D|} \mathrm{Gini}(D^v)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">i</span><span class="mord mathrm">I</span><span class="mord mathrm">n</span><span class="mord mathrm">d</span><span class="mord mathrm">e</span><span class="mord mathrm">x</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">a</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:3.0954490000000003em;vertical-align:-1.267113em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.8283360000000002em;"><span style="top:-1.882887em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.050005em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">&#x2211;</span></span></span><span style="top:-4.3000050000000005em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">a</span><span class="mord mtight">.</span><span class="mord mathdefault mtight" style="margin-right:0.22222em;">V</span></span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:1.267113em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="mord">&#x2223;</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">&#x2223;</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.664392em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span></span></span></span></span></span></span></span></span><span class="mord">&#x2223;</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.936em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">i</span></span><span class="mopen">(</span><span class="mord"><span class="mord mathdefault" style="margin-right:0.02778em;">D</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7143919999999999em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight" style="margin-right:0.03588em;">v</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p>
<p><span class="highlight">&#x9009;&#x62E9;&#x57FA;&#x5C3C;&#x6307;&#x6570;&#x6700;&#x5C0F;&#x7684;&#x5C5E;&#x6027;&#x4F5C;&#x4E3A;&#x6700;&#x4F18;&#x5212;&#x5206;&#x5C5E;&#x6027;&#x3002;</span></p>
<h4 class="mume-header" id="eaxmple">Eaxmple</h4>

<table>
<thead>
<tr>
<th>Day</th>
<th>Outlook</th>
<th>Temperature</th>
<th>Humidity</th>
<th>Wind</th>
<th>Decision</th>
</tr>
</thead>
<tbody>
<tr>
<td>1</td>
<td>Sunny</td>
<td>Hot</td>
<td>High</td>
<td>Weak</td>
<td>No</td>
</tr>
<tr>
<td>2</td>
<td>Sunny</td>
<td>Hot</td>
<td>High</td>
<td>Strong</td>
<td>No</td>
</tr>
<tr>
<td>3</td>
<td>Overcast</td>
<td>Hot</td>
<td>High</td>
<td>Weak</td>
<td>Yes</td>
</tr>
<tr>
<td>4</td>
<td>Rain</td>
<td>Mild</td>
<td>High</td>
<td>Weak</td>
<td>Yes</td>
</tr>
<tr>
<td>5</td>
<td>Rain</td>
<td>Cool</td>
<td>Normal</td>
<td>Weak</td>
<td>Yes</td>
</tr>
<tr>
<td>6</td>
<td>Rain</td>
<td>Cool</td>
<td>Normal</td>
<td>Strong</td>
<td>No</td>
</tr>
<tr>
<td>7</td>
<td>Overcast</td>
<td>Cool</td>
<td>Normal</td>
<td>Strong</td>
<td>Yes</td>
</tr>
<tr>
<td>8</td>
<td>Sunny</td>
<td>Mild</td>
<td>High</td>
<td>Weak</td>
<td>No</td>
</tr>
<tr>
<td>9</td>
<td>Sunny</td>
<td>Cool</td>
<td>Normal</td>
<td>Weak</td>
<td>Yes</td>
</tr>
<tr>
<td>10</td>
<td>Rain</td>
<td>Mild</td>
<td>Normal</td>
<td>Weak</td>
<td>Yes</td>
</tr>
<tr>
<td>11</td>
<td>Sunny</td>
<td>Mild</td>
<td>Normal</td>
<td>Strong</td>
<td>Yes</td>
</tr>
<tr>
<td>12</td>
<td>Overcast</td>
<td>Mild</td>
<td>High</td>
<td>Strong</td>
<td>Yes</td>
</tr>
<tr>
<td>13</td>
<td>Overcast</td>
<td>Hot</td>
<td>Normal</td>
<td>Weak</td>
<td>Yes</td>
</tr>
<tr>
<td>14</td>
<td>Rain</td>
<td>Mild</td>
<td>High</td>
<td>Strong</td>
<td>No</td>
</tr>
</tbody>
</table>
<p><strong>&#x8BA1;&#x7B97;<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">I</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi></mrow><mo stretchy="false">(</mo><mi>O</mi><mi>u</mi><mi>t</mi><mi>l</mi><mi>o</mi><mi>o</mi><mi>k</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathrm{GiniIndex}(Outlook)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">i</span><span class="mord mathrm">I</span><span class="mord mathrm">n</span><span class="mord mathrm">d</span><span class="mord mathrm">e</span><span class="mord mathrm">x</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault">u</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03148em;">k</span><span class="mclose">)</span></span></span></span></strong></p>
<table>
<thead>
<tr>
<th>Outlook</th>
<th>Number</th>
<th>Yes</th>
<th>No</th>
</tr>
</thead>
<tbody>
<tr>
<td>Sunny</td>
<td>5</td>
<td>2</td>
<td>3</td>
</tr>
<tr>
<td>Overcast</td>
<td>4</td>
<td>4</td>
<td>0</td>
</tr>
<tr>
<td>Rain</td>
<td>5</td>
<td>3</td>
<td>2</td>
</tr>
</tbody>
</table>
<ul>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi></mrow><mo stretchy="false">(</mo><mi>O</mi><mi>u</mi><mi>t</mi><mi>l</mi><mi>o</mi><mi>o</mi><mi>k</mi><mo>=</mo><mi>S</mi><mi>u</mi><mi>n</mi><mi>n</mi><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo>&#x2212;</mo><mo stretchy="false">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>2</mn><mn>5</mn></mfrac></mstyle><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>&#x2212;</mo><mo stretchy="false">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>3</mn><mn>5</mn></mfrac></mstyle><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>=</mo><mn>0.48</mn></mrow><annotation encoding="application/x-tex">\mathrm{Gini}(Outlook=Sunny) = 1 - (\dfrac{2}{5})^2 - (\dfrac{3}{5})^2 = 0.48</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">i</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault">u</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mord mathdefault">u</span><span class="mord mathdefault">n</span><span class="mord mathdefault">n</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.00744em;vertical-align:-0.686em;"></span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.00744em;vertical-align:-0.686em;"></span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">4</span><span class="mord">8</span></span></span></span></li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi></mrow><mo stretchy="false">(</mo><mi>O</mi><mi>u</mi><mi>t</mi><mi>l</mi><mi>o</mi><mi>o</mi><mi>k</mi><mo>=</mo><mi>O</mi><mi>v</mi><mi>e</mi><mi>r</mi><mi>C</mi><mi>a</mi><mi>s</mi><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo>&#x2212;</mo><mo stretchy="false">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>4</mn></mfrac></mstyle><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>&#x2212;</mo><mo stretchy="false">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>0</mn><mn>4</mn></mfrac></mstyle><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\mathrm{Gini}(Outlook=OverCast) = 1 - (\dfrac{4}{4})^2 - (\dfrac{0}{4})^2 = 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">i</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault">u</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="mord mathdefault">e</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord mathdefault">a</span><span class="mord mathdefault">s</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.00744em;vertical-align:-0.686em;"></span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.00744em;vertical-align:-0.686em;"></span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span></span></span></span></li>
<li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi></mrow><mo stretchy="false">(</mo><mi>O</mi><mi>u</mi><mi>t</mi><mi>l</mi><mi>o</mi><mi>o</mi><mi>k</mi><mo>=</mo><mi>R</mi><mi>a</mi><mi>i</mi><mi>n</mi><mo stretchy="false">)</mo><mo>=</mo><mn>1</mn><mo>&#x2212;</mo><mo stretchy="false">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>3</mn><mn>5</mn></mfrac></mstyle><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>&#x2212;</mo><mo stretchy="false">(</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>2</mn><mn>5</mn></mfrac></mstyle><msup><mo stretchy="false">)</mo><mn>2</mn></msup><mo>=</mo><mn>0.48</mn></mrow><annotation encoding="application/x-tex">\mathrm{Gini}(Outlook=Rain) = 1 - (\dfrac{3}{5})^2 - (\dfrac{2}{5})^2 = 0.48</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">i</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault">u</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mord mathdefault">a</span><span class="mord mathdefault">i</span><span class="mord mathdefault">n</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.72777em;vertical-align:-0.08333em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.00744em;vertical-align:-0.686em;"></span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">&#x2212;</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span></span><span class="base"><span class="strut" style="height:2.00744em;vertical-align:-0.686em;"></span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:0.64444em;vertical-align:0em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">4</span><span class="mord">8</span></span></span></span></li>
</ul>
<p><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtable rowspacing="0.15999999999999992em" columnalign="left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">I</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">x</mi></mrow><mo stretchy="false">(</mo><mi>O</mi><mi>u</mi><mi>t</mi><mi>l</mi><mi>o</mi><mi>o</mi><mi>k</mi><mo stretchy="false">)</mo><mo>=</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr></mtable><mtable rowspacing="0.15999999999999992em" columnalign="left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>5</mn><mn>14</mn></mfrac></mstyle><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi></mrow><mo stretchy="false">(</mo><mi>O</mi><mi>u</mi><mi>t</mi><mi>l</mi><mi>o</mi><mi>o</mi><mi>k</mi><mo>=</mo><mi>S</mi><mi>u</mi><mi>n</mi><mi>n</mi><mi>y</mi><mo stretchy="false">)</mo><mo>+</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>4</mn><mn>14</mn></mfrac></mstyle><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi></mrow><mo stretchy="false">(</mo><mi>O</mi><mi>u</mi><mi>t</mi><mi>l</mi><mi>o</mi><mi>o</mi><mi>k</mi><mo>=</mo><mi>O</mi><mi>v</mi><mi>e</mi><mi>r</mi><mi>C</mi><mi>a</mi><mi>s</mi><mi>t</mi><mo stretchy="false">)</mo><mo>+</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>5</mn><mn>14</mn></mfrac></mstyle><mrow><mi mathvariant="normal">G</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi></mrow><mo stretchy="false">(</mo><mi>O</mi><mi>u</mi><mi>t</mi><mi>l</mi><mi>o</mi><mi>o</mi><mi>k</mi><mo>=</mo><mi>R</mi><mi>a</mi><mi>i</mi><mi>n</mi><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>=</mo><mstyle displaystyle="true" scriptlevel="0"><mfrac><mn>12</mn><mn>35</mn></mfrac></mstyle><mo>&#x2248;</mo><mn>0.343</mn></mrow></mstyle></mtd></mtr></mtable></mrow><annotation encoding="application/x-tex">\begin{array}{l}
    \mathrm{GiniIndex}(Outlook) =  \\ \\\\ \\\\ \\\\ \\\\
\end{array}
\begin{array}{l}
        \dfrac{5}{14}\mathrm{Gini}(Outlook=Sunny) + 
\\\\    \dfrac{4}{14}\mathrm{Gini}(Outlook=OverCast) + 
\\\\    \dfrac{5}{14}\mathrm{Gini}(Outlook=Rain)
\\\\    = \dfrac{12}{35} &#x2248; 0.343
\end{array}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:11.629759999999997em;vertical-align:-5.564879999999999em;"></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:5.6499999999999995em;"><span style="top:-7.81em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">i</span><span class="mord mathrm">I</span><span class="mord mathrm">n</span><span class="mord mathrm">d</span><span class="mord mathrm">e</span><span class="mord mathrm">x</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault">u</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03148em;">k</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span></span></span><span style="top:-6.609999999999999em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-5.409999999999999em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-4.209999999999999em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-3.0099999999999985em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.8099999999999985em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-0.6099999999999983em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:0.590000000000001em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:1.7900000000000003em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:5.15em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:6.064879999999999em;"><span style="top:-8.064879999999999em;"><span class="pstrut" style="height:3.32144em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">i</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault">u</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault" style="margin-right:0.05764em;">S</span><span class="mord mathdefault">u</span><span class="mord mathdefault">n</span><span class="mord mathdefault">n</span><span class="mord mathdefault" style="margin-right:0.03588em;">y</span><span class="mclose">)</span><span class="mord">+</span></span></span><span style="top:-6.538879999999999em;"><span class="pstrut" style="height:3.32144em;"></span><span class="mord"></span></span><span style="top:-4.8574399999999995em;"><span class="pstrut" style="height:3.32144em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">4</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">i</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault">u</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault" style="margin-right:0.03588em;">v</span><span class="mord mathdefault">e</span><span class="mord mathdefault" style="margin-right:0.02778em;">r</span><span class="mord mathdefault" style="margin-right:0.07153em;">C</span><span class="mord mathdefault">a</span><span class="mord mathdefault">s</span><span class="mord mathdefault">t</span><span class="mclose">)</span><span class="mord">+</span></span></span><span style="top:-3.3314399999999993em;"><span class="pstrut" style="height:3.32144em;"></span><span class="mord"></span></span><span style="top:-1.649999999999999em;"><span class="pstrut" style="height:3.32144em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mord">4</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">5</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord"><span class="mord mathrm">G</span><span class="mord mathrm">i</span><span class="mord mathrm">n</span><span class="mord mathrm">i</span></span><span class="mopen">(</span><span class="mord mathdefault" style="margin-right:0.02778em;">O</span><span class="mord mathdefault">u</span><span class="mord mathdefault">t</span><span class="mord mathdefault" style="margin-right:0.01968em;">l</span><span class="mord mathdefault">o</span><span class="mord mathdefault">o</span><span class="mord mathdefault" style="margin-right:0.03148em;">k</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord mathdefault" style="margin-right:0.00773em;">R</span><span class="mord mathdefault">a</span><span class="mord mathdefault">i</span><span class="mord mathdefault">n</span><span class="mclose">)</span></span></span><span style="top:-0.12399999999999894em;"><span class="pstrut" style="height:3.32144em;"></span><span class="mord"></span></span><span style="top:1.5574399999999988em;"><span class="pstrut" style="height:3.32144em;"></span><span class="mord"><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.32144em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">3</span><span class="mord">5</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mord">2</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">&#x2248;</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span><span class="mord">.</span><span class="mord">3</span><span class="mord">4</span><span class="mord">3</span></span></span></span><span class="vlist-s">&#x200B;</span></span><span class="vlist-r"><span class="vlist" style="height:5.564879999999999em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span></span></span></span></span></p>
<h2 class="mume-header" id="%E7%AE%97%E6%B3%95">&#x7B97;&#x6CD5;</h2>

<h3 class="mume-header" id="id3">ID3</h3>

<p>&#x6BCF;&#x6B21;&#x5212;&#x5206;&#x9009;&#x53D6;<strong>&#x4FE1;&#x606F;&#x589E;&#x76CA;</strong>&#x6700;&#x9AD8;&#x7684;&#x5C5E;&#x6027;&#x4E3A;&#x5212;&#x5206;&#x6807;&#x51C6;&#x3002;</p>
<h3 class="mume-header" id="c45">C4.5</h3>

<p>&#x5148;&#x4ECE;&#x5019;&#x9009;&#x5C5E;&#x6027;&#x4E2D;&#x627E;&#x51FA;<strong>&#x4FE1;&#x606F;&#x589E;&#x76CA;</strong>&#x9AD8;&#x4E8E;&#x5E73;&#x5747;&#x6C34;&#x5E73;&#x7684;&#x5C5E;&#x6027;&#xFF0C;&#x518D;&#x4ECE;&#x4E2D;&#x9009;&#x62E9;<strong>&#x589E;&#x76CA;&#x7387;</strong>&#x6700;&#x9AD8;&#x7684;&#x3002;</p>
<h3 class="mume-header" id="cart">CART</h3>

<p>&#x4F18;&#x5148;&#x9009;&#x62E9;<strong>&#x57FA;&#x5C3C;&#x6307;&#x6570;</strong>&#x5C0F;&#x7684;&#x5C5E;&#x6027;&#x3002;</p>
<h2 class="mume-header" id="%E5%89%AA%E6%9E%9D">&#x526A;&#x679D;</h2>

<p>&#x907F;&#x514D;&#x8FC7;&#x62DF;&#x5408;&#x7684;&#x4E3B;&#x8981;&#x624B;&#x6BB5;</p>
<ul>
<li>&#x9884;&#x526A;&#x679D;&#xFF1A;&#x51CF;&#x5C11;&#x8BAD;&#x7EC3;&#x6D4B;&#x8BD5;&#x65F6;&#x95F4;&#xFF0C;&#x4F46;&#x6709;&#x6B20;&#x62DF;&#x5408;&#x98CE;&#x9669;&#x3002;</li>
<li>&#x540E;&#x526A;&#x679D;&#xFF1A;&#x6CDB;&#x5316;&#x6027;&#x80FD;&#x4E00;&#x822C;&#x4F18;&#x4E8E;&#x9884;&#x526A;&#x679D;&#xFF0C;&#x4F46;&#x8BAD;&#x7EC3;&#x5F00;&#x9500;&#x5927;&#x3002;</li>
</ul>

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